Shutdown the container

# lxc-stop -n $NAME
Archive container rootfs & config

# cd /var/lib/lxc/$NAME/

# tar --numeric-owner -czvf container_fs.tar.gz ./*

# rsync -avh container_fs.tar.gz user@newserver:/var/lib/lxc/

Extract rootfs

# mkdir /var/lib/lxc/$NAME/
# cd /var/lib/lxc/$NAME/
# tar --numeric-owner -xzvf container_fs.tar.gz .

https://stackoverflow.com/questions/23427129/how-do-i-backup-move-lxc-containers